4. (28 marks) Consider an LTI continuous-time system, whose input x(t) and output y(t) are related by (d^2 y(t))/(dt^2) + 3(dy(t))/dt + 2y(t) = x(t) (a)Determine a possible expression for the system transfer function H(s) and indicate its zeros and poles. (b)List all the possible ROCs , and determine all the corresponding unit impulse responses. (c)If the system is causal. Calculate the output signal that is caused purely by the input signal x(t) = u(t).
Added by Robert M.
Close
Step 1
(a) To determine the transfer function H(s), we can take the Laplace transform of both sides of the given equation: 4V(s)s^2 + 3dy(s)s + 2y(s) = X(s) Rearranging and solving for V(s)/X(s), we get: V(s)/X(s) = 1/(4s^2 + 3ds + 2) This is the transfer function Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 88 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Consider an LTI system whose input x(t) and output y(t) are related by (d^2y(t))/(dt^2) + 3(dy(t))/(dt) + 2y(t) = x(t). (a)Determine a possible expression for the system transfer function H(s) and indicate its zeros and poles. (b)List all the possible ROCs and determine all the corresponding unit impulse responses. (c)If the system is causal, calculate the output signal that is caused purely by the input signal x(t) = u(t).
Adi S.
Sri K.
An LTI system with input signal x(t) = [e^t + e^{-2t}] u(t) gives the response y(t) = [2 - 3t] e^{-2t}u(t) (a) Find the transfer function of this system, i.e., H(s). (b) Determine the impulse response of the system, i.e., h(t).
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD